Branco J R, Ferreira J A, de Oliveira Paula
CMUC & Polytechnic Institute of Coimbra, ISEC, DFM, Coimbra, Portugal.
CMUC & Department of Mathematics, University of Coimbra, Coimbra, Portugal.
Math Biosci. 2014 Sep;255:83-90. doi: 10.1016/j.mbs.2014.07.002. Epub 2014 Jul 21.
In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included.
在本文中，我们提出了一个数学模型来描述考虑脑组织粘弹性特性的胶质瘤细胞的演化。该数学模型的建立是基于胶质瘤细胞有两种表型：迁移型和增殖型这一考虑。迁移细胞的演化由一个非菲克型的扩散反应方程描述，该方程是在考虑具有非菲克迁移质量通量的质量守恒定律的情况下推导出来的。增殖细胞的演化由一个反应方程描述。给出了一个稳定性分析，该分析有助于设计高效的方案。还包括了说明该数学模型行为的数值模拟。
